Effects of Spin-orbit Coupling on Superconducting Pairing Interactions

Superconductors with spin-orbit coupling exhibit many fascinating properties, including abnormally high upper critical fields and possible topological excitations. These effects are recognized as originating from the impact of spin-orbit coupling on the Cooper pair wave function.

In contrast, how spin-orbit coupling affects the superconducting pairing interactions – the glue that binds electrons together in Cooper pairs – remains an open question.

This is particularly relevant in unconventional superconductors as the interplay between spin-orbit coupling and electronically mediated superconducting pairing interactions may give rise to novel feedback effects that boost the efficacy of the pairing interactions.In this project, I will adopt a dual-pronged approach to study the interplay between spin-orbit coupling and interactions: (1) Develop a generalized Eliashberg theory to account for feedback effects in spin-orbit coupled systems and (2) implement fermionic renormalization group methods and determinant Quantum Monte Carlo simulations to map out the interplay between electronic correlations and spin-orbit coupling.The main results of SuperSOC will be:- Establishing how spin-orbit coupling may fundamentally reshape the pairing interactions and modify the associated superconducting instabilities of unconventional superconductors.- Developing a framework for studying these feedback effects in material-specific models and employing this to understand the phase diagrams of unconventional spin-orbit coupled superconductors.- Demonstrating how the interplay between electronic correlations and spin-orbit coupling leads to anisotropic interactions that alter the shape of the electronic phase diagram and may enhance pairing.These achievements pave the way for identifying the nature and origin of unconventional superconductivity in spin-orbit coupled systems and enable a determination of the electronic phase diagrams in such systems.